Hey there, I've been looking through my maths work that we've done so far (C1 obviously) and I'm up to completing the square and I just don't get what to do, I can't work out what I'm doing from my own notes. I looked at a textbook and still don't really get it.

Theres a few different types of questions from the textbook, the questions sort of build up as you go through it (core maths for advanced level)

So the first set say: Add a number to each expression so that the result contains a perfect square as a factor. (I don't really know what I'm supposed to be doing)
Heres an e.g. of a question: x^2 - 4x, another is 2x^2 - 4x, and so on.

But here are by the looks of it the main type of question: Solve the equations by completing the square, giving the solutions are in surd form:
I'll try and give a variation of questions...

1. X^2 + 8x = 1
2. 2X^2 - x - 2 = 0
3. 2x^2 + 4x = 7

But yeah, if anyone could show me one of those examples with all the steps explained I'd be grateful, because I really don't know what I'm doing! What is actually meant by completing the square?
The answers are in the back of the textbook but of course there are no steps so its pretty useless for me to write the answer straight down.
Thanks a lot

The Song
This is how we complete the square
Complete the square
Complete the square
This is how we complete the square
Of a simple quadratic function

Half the coefficient of x
efficient of x
efficient of x
Half the coefficient of x
Then subtract its square from the constant.

What it actually means
So, always arrange the equation into the form like 2x^2 + 5x + 13 = 0
Then divide everything by the coefficient of x^2, to get 2(x^2 + 5/2x + 13/2) = 0
Then complete the square on the (x^2 + 5/2x + 13/2) part

"Half the coefficient of x"
Half of 5/2 is 5/4, right?
Then put this 5/4 in a bracket like so: (x-5/4)^2. Step one done.

"Then subtract its square from the constant"
i.e. subtract (5/4)^2 from the original constant, which was 13/2- thus leaving us with 13/2 - (5/4)^2. Step 2 done.

Then we add the two parts formed together.
So x^2 + 5/2x + 13/2 = (x-5/4)^2 + (13/2 - (5/4)^2)

(Original post by Icy_Mikki)The Song
This is how we complete the square
Complete the square
Complete the square
This is how we complete the square
Of a simple quadratic function

Half the coefficient of x
efficient of x
efficient of x
Half the coefficient of x
Then subtract its square from the constant.

What it actually means
So, always arrange the equation into the form like 2x^2 + 5x + 13 = 0
Then divide everything by the coefficient of x^2, to get 2(x^2 + 5/2x + 13/2) = 0
Then complete the square on the (x^2 + 5/2x + 13/2) part

"Half the coefficient of x"
Half of 5/2 is 5/4, right?
Then put this 5/4 in a bracket like so: (x-5/4)^2. Step one done.

"Then subtract its square from the constant"
i.e. subtract (5/4)^2 from the original constant, which was 13/2- thus leaving us with (5/4)^2 - 13/2. Step 2 done.

Wow, thats actually pretty easy when broken down! Thanks a lot, can anyone find me any links to questions on CTS? Not ones that involve CTS, but just an equation, or perhaps some of you could give me some?
Thanks